Strange though it must seem to their opponents, some Conservatives will travel to Birmingham for their conference this weekend uncertain whether their party political glass is half full or half empty. Back in government the Tories may be, but having hoped for outright victory for so long, and having accepted as fact the poll predictions of narrow overall electoral victory, some are still angry that David Cameron failed to deliver on 6 May and ended up in coalition with the Liberal Democrats instead. Many of their complaints come down to Mr Cameron himself: that he tacked too far to the centre; that he cuts the rest of his party too much out of the loop; that he has given up too many cherished rightwing projects for the sake of the coalition. In short, that he presides over a government that is not Tory enough, perhaps not even Tory at all.

These kinds of views get a good showing in the newspapers, magazines and websites of the Tory right. But they are not the centre of gravity of the Tory party itself, never mind of the country – and nor, if the Tories have learned anything from their years in opposition, are they in the Tory interest. The Tories are only where they are today because Mr Cameron recognised the need to change the party and move it to the centre. His reward was 2 million more votes for the Tories compared with 2005 and the party's largest increase of seats at any election for 80 years. The Tory failure to do better was not due to Mr Cameron's modernisation and centrism but to his failure to persuade enough voters that they were credible. Throughout the election, the Tories struggled to push their share of the vote above a glass ceiling in the upper 30s – and still do today. The question that faces the Tories in Birmingham, therefore, is whether and how they can consolidate what Mr Cameron has given them, and then do better.

The essential answer is to stand by their man and his pragmatism, and not allow themselves to be tempted to the right. In the medium term, this is wholly bound up with the spending review that George Osborne will announce on 20 October. That package has always been too large, too rapid and too inflexible for economic safety, and thus threatens to hit the coalition parties hard in the ballot box. How hard it will do so is difficult to predict: this week's Guardian/ICM poll showed a large majority trusting the coalition to take the right economic decisions, alongside a narrower majority for the view that the plans go too far rather than get the balance right. Either way, however, it is extremely important for the coalition that the package is now constructed in the least unfair way (though cuts to services on which the poor most depend can never be considered as fair) and that ministers give no encouragement this week to the idea that they are engaged in an ideologically driven, rather than a necessity-driven, exercise. The signs are mixed. The speeches, debates and interviews which ministers give in Birmingham will be measured against this test.

Naturally, most Tory voters would prefer their party to govern alone. Most of the activists would too. That's why they support their particular party. Yet one of the most striking findings of this week's Guardian/ICM opinion poll is that 41% of current Conservative and Liberal Democrat voters alike already believe that the country is best governed by the current coalition rather than by any party governing alone. Two weeks ago in Liverpool, the Lib Dems managed to flex their own ideological muscles occasionally while at the same time showing themselves overwhelmingly committed to the pragmatic give and take of coalition. One of the important wider tests of the coming week is whether the Tory party, historic coalition sceptics, can do the same thing. If the answer is yes, the coalition's prospects are good. If the Tories spend the week complaining about the Lib Dems, never mind Mr Cameron, they will do themselves no favours at all.